How do I actually play with it? I am not sure what files I can work with or how to even make a design.
I'd check this link out, 101 Getting Started Guide
But to fiddle with it, click the Artboard and hit enter to get a box.
What are some of the things I should be able to create using Subform? All I can get to is creating the different color blocks on top of eachother.
As @rrbarry11 said, read through that getting started guide and watch the videos (included in the first paragraph or so), I've posted one below.
Subform is very much based on parent-child relationships. So, in the instance where you've got different color blocks on top of each other, you likely have those colors blocks sitting in an artboard, and then you're defining the relationship of those blocks (ie. stacking on top of each other).
Just watch the video, hopefully that explains.